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 Feb27 awarded Curious Feb26 asked Representation Matrix computation time estimation Dec24 awarded Tumbleweed Dec17 asked Determine the valuation of $\rho$ with $F = k(x,\rho)$ at the only place above $(\infty)$. Nov12 accepted Prime ideal $P$ in $R$ coprime to the conductor plus the localization $R_{P}$ is a DVR implies that $P$ is invertible Nov12 comment Prime ideal $P$ in $R$ coprime to the conductor plus the localization $R_{P}$ is a DVR implies that $P$ is invertible The source is part of some lecture notes from my professor and therefore I wasn't sure if I'm allowed to put that here; besides it's written in german. And yes, $P + \mathcal{F} = B$ was used to show that $B_P$ is a DVR. Again, thank you very much! Nov12 comment Prime ideal $P$ in $R$ coprime to the conductor plus the localization $R_{P}$ is a DVR implies that $P$ is invertible I thought about this before but I kind of scrapped that idea for no reason. Of course this is the answer, it's clear now! Thank you very much. Nov12 asked Prime ideal $P$ in $R$ coprime to the conductor plus the localization $R_{P}$ is a DVR implies that $P$ is invertible Jul31 awarded Teacher Jul25 comment Why is every Divisor of the rational function field $K(x)$ over $K$ a principal divisor if $K$ is algebraically closed So the statement is wrong as I suggested. Because the degree of a prime divisor is 1. Jul24 asked Why is every Divisor of the rational function field $K(x)$ over $K$ a principal divisor if $K$ is algebraically closed Jun5 comment What is meant by $|dxdy|^{1/2}$ in the integral? What does the symbol $\wedge$ mean and thus $dx \wedge dy$? Jun5 comment What is meant by $|dxdy|^{1/2}$ in the integral? And how would this expression change under changes of coordinates? I'm sorry if this is fundamental, but I'm not very familiar with analysis this deep. We had the projective coordinates: $x = x$ and $s = y/x$. So how would the written object change under the change of coordinates to those above? Jun5 asked What is meant by $|dxdy|^{1/2}$ in the integral? Apr16 comment Characterization of transcendental elements in algebraic function fields @ YACP: Thank you very much for your help! Apr16 accepted Characterization of transcendental elements in algebraic function fields Apr16 comment Characterization of transcendental elements in algebraic function fields Now I got it. If $z$ is transcendental over $K(X)$, then $K(z) \cong K(X)$ and $X$ is clearly algebraic over $K(X)$ since $X\cdot X^1 + X^2 \cdot X^0 = 0$ and $X \neq 0$ and $X^2 \neq 0$. Apr16 comment Characterization of transcendental elements in algebraic function fields To the second part: Why is $z$ algebraic over $K(X)$, if $z$ is transcendental over $K$? EDIT: I haven't met him yet. Apr15 comment Characterization of transcendental elements in algebraic function fields Does this change the situation to a convincing one? And yes, I'm new to field theory. Apr15 awarded Editor